<h2>Problem 213</h2>
<div style="color:#666;font-size:80%;">18 October 2008</div><br />
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<p>A 30<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />30 grid of squares contains 900 fleas, initially one flea per square.<br />
When a bell is rung, each flea jumps to an adjacent square at random (usually 4 possibilities, except for fleas on the edge of the grid or at the corners).</p>

<p>What is the expected number of unoccupied squares after 50 rings of the bell? Give your answer rounded to six decimal places.</p>
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